The BFD equation is a modification of the classical Boltzmann equation, when we account for the quantum effects of molecular encounters. In some other literatures, BFD equation is also frequently called Uehling-Uhlenbeck equation or Nordheim equation. At variance with the derivation of the classical Boltzmann equation [1]}, [2]}, the rigorous derivation of the BFD equation is yet to be established. Since it was presented in Nordheim [3]}, Uehling and Uhlenbeck [4]} by heuristic arguments, works on the derivation of the BFD equation have been taking lots of time.
